I was well into high school before I got my hands on an old engineering textbook with a section on "estimating" with tricks about fractions. For example, each part of 1/6 is 16.67% - but 2/6, 3/6 and 4/6 are all equivalent to more commonly known fractions of 1/3, 1/2 and 2/3. So to know the percentage of all "sixths", you just need to learn 1/6 and 5/6 (at 83.3%). For sevenths, you just memorize the sequence 142857 - this is the repeating decimal for sevenths and only the starting digits vary. For example, 1/7 = 0.142857, 2/7 = 0.285714, and so on. For ninths, each ninth equals 0.1111, and for elevenths, each elevenths equals 0.09090909

With memorizing these fractions, it's easy to estimate the percentage of any fraction. We could have been taught this years ago - every time we had a math test, everyone would want to know what percentage grade they got. Teachers didn't particularly score their tests out of even numbers, so if you got 47 out of 57, you could either get a calculator or do some long division. So the estimating tricks involved rounding to even numbers, reducing fractions, and then using those memorized tricks. For 47/57, it's pretty close to 48/58 - reduced that to 24/29, which is close to 24/30 = 8/10 or about 80%. Or you can round to 48/56, or 24/28, which reduces to 12/14 then 6/7. Using the trick above, 6/7 = 85.7142%, so we have now established an upper and lower bound for the estimate - split the difference and you get about 82.5% - the real value of 47/57 is 82.456%. It's all simple mental math and you really only ever divide by 2 or 3.

When I took a technical drawing class in high school, the rest of the class was constantly throughout the period asking me to convert power-of-two fractions into decimal for them. Which for a relatively small power of two (we rarely had to deal with less than X/32) is actually quite easy to do. Not a long string of numbers like 1/7th. One of them said I must spend hours memorizing every possible fraction. In fact I only knew them from dealing with them in class the same way they had done, except instead of plugging it into a calculator or asking me, I took a moment to figure out how simple it is.

I hadn't heard of anyone thinking ⅓ was smaller that ╝ but I can believe it. In 2007, the company that runs the UK's lottery had to withdraw a scratchcard game they were running because too many people were struggling with the maths involved.

Of course 1/3 is more than 1/4..and 30% is more than 40%.
Seriously though, I had a fellow student in Drafting/Design and Technology ask me what half of 1/8 is, I told her 1/16 and she insisted that couldn't be true because 16 is twice as much as 8. There is a certain logic to her ignorance.

Seriously though, I had a fellow student in Drafting/Design and Technology ask me what half of 1/8 is, I told her 1/16 and she insisted that couldn't be true because 16 is twice as much as 8. There is a certain logic to her ignorance.

And that is why math education should include more than just knowing how to get an answer, but lots and lots of practice, converting math facts into charts, graphs, and other representations, and rote memorization of at least the core math facts required by the decimal system (such as the addition and mulitplication tables up to 10). Your acquaintance could probably have worked through figuring out that 1/16 was the right answer (like Plato teaching the slave to square 2), but in real life most people's math is snap impressions, and it would be helpful to the person and society if people could make better conclusions on such things on the fly (and recognize on the fly when something needs further thought).

As a kid who stuggled in grade school in with math, graphs and charts did not help me. I felt like I was being asked to memorize pretend systems in hieroglyphs that didn't have anything to do with reality. I needed the apple and marble demonstrations. Once I saw the practicality of math, the solidness of it, I believed it in. I even snuck into the kitchen to test the measuring cups. Before that I was a skeptic.

I was cooking last night and looked through the drawer. The 1/4 cup on all four of my nesting sets has gone awol. I'm fortunate that I can eyeball well enough on a 1/3 cup to get the right ratio

The reason for still having a ⅓ cup measure could be due to its being a measurement less often occurring in recipes. That, combined with the possibility that people who eat fast food are less likely to cook for themselves and use measuring cups, may account for people's confusion.

Quote:

Originally Posted by UEL

I know people that look a a jar of peanut butter, 900 grams $8. And another one 500 grams $5, and think they are getting the better deal with the 500 gram jar, because it costs less.

Stores don't always help.

I ate a restaurant once where a full order of four potato pancakes was $3.99, while a half order of two was $1.75.

Quote:

Originally Posted by crocoduck_hunter

I like A&W hamburgers all right, but it's not a place that I'd really go to for a hamburger because of how long it's always taken to get my food every time I've gone. I've I'm going to a fast food restaurant (which I try to avoid), I want my food quickly and the local A&W has never done that in my experience.

I grew up with A&W drive-in restaurants and their Burger Family members: Papa Burger, Mama Burger, Teen Burger, and Baby Burger. Their burgers were great. In the seventies, they started selling the root beer at stores, while most of the restaurants disappeared. When one reappeared briefly around the turn of the century, it was inside a convenience store. The burgers were still great, although Papa Burger, who had now grown from ╝lb. to ⅓lb., was the only family member left by name. Teen Burger had similarly grown and become Original Bacon Double Cheeseburger, Mama Burger had shed her lettuce, tomato, and onion, having changed her name to Cheeseburger, while Baby Burger was now referred to as Hamburger. The service was very slow.